Mathematical model for parametric tooth profile of spur gear using line of action

A mathematical model for parametric tooth profile of spur gear is proposed by using a given equation of line of action. The line of action usually comprises only simple curves. It will be easier to manipulate the line of action when multisegment tooth profile curves are used. The proposed mathematical model will enhance the freedom of tooth profile design by combining the simple curves into the line of action. The curvature, sliding velocity, contact ratio, and the limitation of undercutting can be derived directly from the equation of line of action. Based on the proposed mathematical model, we can represent both mating tooth profiles by the single parameter of line of action. Therefore, it is easier to study the kinematical characteristics of mating gears with nonstandard tooth profiles by applying the proposed mathematical model.